A171245 Reciprocals of the deviation of continued fraction convergents from Pi.

7, -790, 12016, -3748629, 1730431227, -3015428685, 8172837003, -34313104062, 114738541304, -620832653094, 2474837590227, -45157370341559, 1726856191927439, -6094457427533473, 12791098836150787, -51642743340781227, 325724575136738920, -1813676066719263909

Offset

1,1

Comments

Clearly the terms alternate in sign, but the initial choice of sign was arbitrary.

Links

Table of n, a(n) for n=1..18.

Example

The first convergent to Pi, 3, is just over 1/7 too low, so 7 is the first term.
The second convergent, 22/7, is 0.001264+ too high, which is just over 1/790, so -790 is the second term.

Prog

(PARI) for(x=1, 10, t=contfracpnqn(contfrac(Pi, x)); print(truncate(1/(Pi-t[1, 1]/t[2, 1]))))

Crossrefs

Cf. A001203.

Sequence in context: A162089 A020470 A182282 * A014013 A001467 A342836

Adjacent sequences: A171242 A171243 A171244 * A171246 A171247 A171248

Keyword

sign

Author

Phil Carmody, Dec 06 2009

Extensions

More terms from Jinyuan Wang, Aug 23 2021

Status

approved